The efficiency of a conventional air pump of the early model is rather limited in that the pumping of air is effected in a one-way manner that the air is driven into something, such as a tire, only when the piston of the pump is driven to move in a specific direction. However, such a conventional air pump was improved to an extent that the pumping of air could take place in a two-way fashion when the piston of the pump was caused to make a reciprocating motion. In order to improve further the efficiency and the effect of the conventional air pumps, the cylinders of the air pumps were diametrically enlarged to allow a greater amount of air to be driven into a tire and the like. However, such an improvement as mentioned above is also limited in that the pumping effect and the pumping efficiency are both undermined because the cross-sectional area of the pump cylinder is inversely proportional to the pressure, thereby causing a person to encounter with a difficulty in pumping even when the tire pressure has not reached a required level.